Tohoku Mathematical Journal 2015 December SECOND SERIES VOL. 67, NO. 4

 Tohoku Math. J. 67 (2015), 573-584

Title STRONG CONVERGENCE THEOREM OF CESÀRO MEANS WITH RESPECT TO THE WALSH SYSTEM

Author István Blahota, Giorgi Tephnadze and Rodolfo Toledo

(Received April 11, 2014, revised July 18, 2014)
Abstract. We prove that Cesàro means of one-dimensional Walsh-Fourier series are uniformly bounded operators in the martingale Hardy space $H_p$ for $0<p<1/(1+\alpha).$

Mathematics Subject Classification. Primary 42C10.

Key words and phrases. Walsh system, Cesàro mean, martingale Hardy space.